Question

Can someone please please help me i finished everything besides the last question (medal and fan)

Answer 1

Which f(x) are we using for part 4?

Answer 2

idk thats what im confused about

Answer 3

I'm assuming since the first f(x) was listed BEFORE the questions, it applies to all four of them. So let's use that one.

I'm a lil confused on the function though.
Maybe some of the stuff didn't get printed correctly.
Is this what it's supposed to look like?\[\Large\rm f(x)=25(1.08)^x\]

Answer 4

no the 1.08 is supposed to be 1.3

Answer 5

\[\Large\rm f(x)=25(1.3)^x\]Like that? :\
I don't see that anywhere but if that's what you think is right.
Should we go with 25 or 23?

Answer 6

i wasnt trying to copy other peoples work and 23

Answer 7

\[\Large\rm f(x)=23(1.3)^x\]Ok c: So let's see...

Answer 8

Replacing x with x+2,
\[\Large\rm f(x+2)=23(1.3)^{(x+2)}\]This will shift the function 2 to the left.
That doesn't really explain much for us though.
Let's get it into the form where we only have an x in the exponent.

The way we do that is by using rules of exponents!

Answer 9

There is a rule that allows us to write the addition like this:
\[\Large\rm (1.3)^{x+2}=(1.3)^x\cdot(1.3)^2\]

Answer 10

1.69 is 1.3 squared

Answer 11

Ok let's combine that with our 23 by multiplying.

Answer 12

f(x+2) = ? is it gonna just be 1.69 or 1.69^x

Answer 13

This is what we've determined so far using our exponent rule,
\[\Large\rm f(x+2)=23(1.3)^{(x+2)}\]\[\Large\rm f(x+2)=23(1.3)^{x}\cdot(1.3)^2\]\[\Large\rm f(x+2)=23(1.3)^{x}\cdot(1.69)\]\[\Large\rm f(x+2)=23(1.69)(1.3)^{x}\]The 1.69 is not being raised to the x power.
We need to multiply the 23 and 1.69 from here, that will tell us something important.

Answer 14

f(x+2) = 38.87 (1.3)^x

Answer 15

Ok great!

Answer 16

For our original f(x),\[\Large\rm f(x)=\color{orangered}{23}(1.3)^x\]This 23 was telling us something really important.
It was telling us the starting price of the stock!
\[\Large\rm f(x+2)=\color{orangered}{38.87}(1.3)^x\]So what can we say about f(x+2)?

Answer 17

idk :/

Answer 18

It looks like it has changed the starting price, yes?

Answer 19

yeah

Answer 20

So yah that takes care of the first one c:
Adding 2 to x increased the starting price to 38.87.

Answer 21

oh ok so we dont change it from there ?

Answer 22

So for this first one, you would want to explain that the starting prices have changed, and that you figured that out using rules of exponents.

Then you have to graph them to compare.
Understand how to graph? Just plot a few points. Make sure you plot the point where x=0.

Answer 23

Yes, we don't change it from there :O
We have two more to do though.

Answer 24

ooh lol yeah the second one looks easy ... i think but do we have to plug something in for x?

Answer 25

\[\Large\rm f(-x)=23(1.3)^{-x}\]For the second one?
So the negative sign is telling us to reflect the function over the y-axis.

Answer 26

We could apply another rule of exponents to get it into the form we're looking for.

Answer 27

I'm going to put a -1 where the negative sign is, so it'll be easier to understand.
\[\Large\rm (1.3)^{-1x}=(1.3^{-1})^x\approx\left(0.77\right)^x\]

Answer 28

When we're multiplying exponents, we can rewrite it as an exponent to an exponent.

Answer 29

wait so do i multiply 23 and 1.3

Answer 30

So this has not affected our starting price at all.
\[\Large\rm f(-x)=23(0.77)^{x}\]But now you can see that the base multiplier is smaller than 1.
So our stock will lose value over time.

Answer 31

No don't touch the 23 for this one :O

Answer 32

oh ok

Answer 33

\[\Large\rm f(-x)=23(1.3)^{-x}\]\[\Large\rm f(-x)=23(1.3^{-1})^{x}\]\[\Large\rm f(-x)=23(0.77)^{x}\]So our stock is not gaining value over time, it's now losing value over time.
And then I'll let you take care of graphing it >.<
I think you can handle it.

Answer 34

Third one? c:

Answer 35

oh lol ok f(x)+3

Answer 36

\[\Large\rm f(x)\qquad~\quad=23(1.3)^x\]\[\Large\rm f(x)+3\quad=23(1.3)^x+3\]

Answer 37

So ummmm...

Answer 38

ohhh i was confused about that

Answer 39

what do we do next

Answer 40

The +3 represents a `vertical shift` upwards by 3.
So every point on our graph f(x) is shifted up by 3.

Our starting amount will be 23+3, so 26 instead of 23.
And every other point will be 3 more than it was before.

Answer 41

If you're able to graph f(x), then this one should be pretty straight forward, just add 3 to each of your y values.

Answer 42

oh ok well thaanks for the help :)

Answer 43

c: